The invention is directed to a centrifugal rpm regulating device for use in a fuel injection apparatus for an internal combustion engine having a governor for control of an injection pump in response to the volume of a work chamber. In an already known rpm regulating device of this general type the work chamber serves to dampen the rpm regulating device. This work chamber is arranged in the interior of the governor sleeve and communicates with the inner chamber of the injection pump which is pressurized via one or more throttle openings. In spite of the advantageous dampening of the rpm regulating device provided by this arrangement, it is necessary for smooth operation of the internal combustion engine to choose the proportional band of the rpm regulating device in such a manner that the idling rpm can fluctuate over an undesirably wide range in actual practice. If, for reasons of fuel economy, the idling rpm is set at a low level, it is possible for the idling rpm to drop too low due to this `softness` of the rpm regulating device resulting in an engine which operates unevenly, noisely or even stops running, the latter caused by the further presence of inertial stress of cold lubricaing oil in the engine, of the actuation of an air conditioner, and/or of an automatic vehicle power assist, or a similar phenomena.